Actually, don't have to chase Wyoming elk points at all if you want to hunt elk in Wyoming as a NR. Could hunt pretty much every year with 0-1 point in quality units for cow elk which are a LOT bigger than doe whitetail.
I never FL size new brass, but will clean up the neck if they look dented. Good idea to chamber the new cases to see if they fit. Sounds like the Nosler cases may be a bit long for your tight 17 Rem chamber like others have said.
If you had measured your Peterson brass with a should comparator...
Yep, case is crimped too much and has compressed the case causing it to bulge out. You need one of these, https://www.midwayusa.com/product/1018249683?pid=429532
Read through the instructions with the dies again. Three die set or four die set? Some of the straight wall pistol die sets have a...